1. Yes you can trade from anywhere, if there is any restriction it won’t be from India, it might be the country where you are trading from. For example Dubai and countries in the gulf have blocked most trading websites.
2. Are you allowed to open a trading account in USA, guess you would have to speak to a brokerage there. But you should be able to.
3. Yes you can trade on US Stocks from India, ICICI direct gives you that option presently.
4. Our trading platform (Zerodha Trader) has live feeds on Currency and Commodity. For EOD prices search for NSE Currency Bhavcopy and MCX Bhavcopy on google, you will find the links.